What is Logic: Definition and 1000 Discussions

Logic (from Greek: λογική, logikḗ, 'possessed of reason, intellectual, dialectical, argumentative') is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.There is no universal agreement as to the exact definition or boundaries of logic (see § Rival conceptions). However, the scope of logic (broadly construed) includes:

The classification of arguments.
The systematic analysis of logical forms.
The systematic study of the validity of deductive inferences.
The strength of inductive inferences.
The study of faulty arguments, such as fallacies.
The study of logical paradoxes.
The study of syntax and semantics of formal languages.
The study of the concepts of meaning, denotation and truth.Historically, logic has been studied mainly in philosophy (since Antiquity), mathematics (since mid-19th century), and computer science (since mid-20th century). More recently, logic has also been studied in linguistics and in cognitive science. Overall, logic remains a strongly interdisciplinary area of study.

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  1. R

    Digital Logic Fundamentals help

    I have recently started my second year at Uni and one of the areas I am studying is Digital Logic Fundamentals. However due to a mixup with my timetable I missed the first few weeks of the course. I am trying to catch up but have become stuck on part of the course that wasn't explained well in...
  2. S

    Second-Order Logic: Understanding the Basics

    I have read, that properties of sets such as that every subset has supremum or that set is well ordered cannot be expressed in the language of first-order logic. Well, when I tried to write these things, I seemed to write them in first order language, which really bothers me. So please, tell me...
  3. S

    How can I simplify this circuit using boolean algebra for XOR and XNOR gates?

    I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible. I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck
  4. A

    How can changing the value of m affect the percentage p?

    Easy to understand problem (please read; I promise you'll understand): I've created my own financial spreadsheet. One of its functions is to allow me to automatically determine how much money I need to save every month m in order to accumulate x dollars in y amount of time. Normally...
  5. H

    How Do AND/OR Logic Gates Work with Diodes?

    http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/diodgate.html Could someone please explain to me why these circuit arrangements act as AND/OR gates, can't find a decent explanation in any of my books
  6. H

    Solving Predicate Logic Proof Problem with Resolution Refutation

    I have a question on my assignment that I'm having a great deal of trouble with. In this question we will consider a simplified model of the “People you may know” application in Facebook. The basic idea is that if two people have a common friend, then they may know each other. We will also...
  7. iamhumble

    Correct Combination Thought Logic Being Followed

    For fun this semester I decided to take a probability class and doing a lot of the random problems from the book to learn the material. I am finding that sometimes I am over complicating some of these problems. Here is a problem I came across. When I punched in the numbers it didn't seemed...
  8. N

    What is the correct answer to this simple maths problem?

    http://img372.imageshack.us/img372/2057/timezy9.jpg See image above. The answer is D - 88, however I can only find 84! Please can someone let me know what I am missing: 20-7= 13 13*6 + 1 = 79 = total upto 2030 + 2045 bus = 80 + 4 buses (two in 21st hr, two in 22nd hr) = 84 Thanks
  9. M

    The logic behind the cross product with units

    The cross product equals to the area of the parallelogram defined by the two vectors (at least in R^3). So if working on vectors which units v_1 = (1,2,3)m v_2 = (3,4,5)m it correctly returns the according area. However, if used to get a vector perpendicular to each of the vectors the...
  10. D

    Who is the tallest, the smallest of the tallest or the tallest of the smallest?

    Hi, I am a french Student in pures sciences. so its a bit hard for me to express myself in english, but I will do my best. Homework Statement Three hundred (300) persons are placed in thirty (3) rows and ten (10) columns. We choose the tallest person of each ROW. Then, we take the...
  11. J

    Basic vending machine logic circuit, with visual

    1. Homework Statement Design a logic circuit to simulate the circuitry that might exist in a vending machine. the vending machine accepts inputs of nickels, dimes, and quarters but only one of each. It dispenses water and beer. Use three logic switches to simulate the coin detectors one each...
  12. J

    Engineering Basic Logic Circuit for a vending machine

    Homework Statement Design a logic circuit to simulate the circuitry that might exist in a vending machine. the vending machine accepts inputs of nickels, dimes, and quarters but only one of each. It dispenses water and beer. Use three logic switches to simulate the coin detectors one each for...
  13. Q

    Need someone to verify my logic

    Homework Statement Find the supremum and infimum of the following sets and test whether these sets have a maximum or minimum: (a) { |x|/(1+|x|) s.t. x is in R} (b) { x/ (1+x) s.t. x > -1}  Homework Equations Order Axioms and Field Axioms for the real numbers; infimum and...
  14. A

    Decidability of -1<1/0<1 using the ordered field axioms and first order logic

    Is the statement -1<1/0<1 decidable using the ordered field/real number axioms and first order logic? I have tried to prove that the statement is either true or false but have had no success since the axioms and theorems only make statements about objects that exist and do not give any clear way...
  15. C

    Logic Gates: Basics & Uses for O-Level Students

    Hi! I'm new to this forum, just joined a couple of hours ago. I am an O-Level student and I am currently on revision leave. I would like some explanations on the basic working principle of logic gates and their uses in special circuits. The clearer the explanation the better and some links to...
  16. D

    India 450,000"Calculating India's Population: Logic & Facts

    How many people are living in India? With the help of following data can you find How many people were listed as living in India and give logic also ? . The population of some countries is calculated based upon some logic and listed here ( It has no link with the facts) :- . USA...
  17. V

    Digital logic circuits material

    could anybody suggest me a good learning material for 'digital logic circuits'
  18. Gib Z

    What Are Some Typical Logic Problems Faced by Beginners?

    Ok well I got a set of 15 logic-ish problems, never really been very good at this stuff. I got about 7 of them fine, but I'll put them up just to check. ------- Q1 999. 998. 997. 996 729. 648. 567. 486 126. 192. 210. 192 12. 18. ? 18 Which Of the following is the missing...
  19. G

    Programs Searching for Interdisciplinary PhD Program on Logic

    Is there any PhD Program in US on logic where I can apply as a student with a computer science background and further combine my interest in logic, philosophy, math and computer science? For now, I only know a program at CMU, which is PhD Program in Pure and Applied Logic.
  20. R

    Logical Riddle: How Many Cars Do I Have?

    All but two of my cars are Fords, all but two of my cars are Toyotas and all but two of my cars are Hondas. How many cars do I have. The obvious answer is three. I'm arguing with some folks that are claiming two is an acceptable answer and they are using the rationale that it is fine to...
  21. A

    Quantum Physics, Causality, and Logic

    Logic and causality? Hi, what implications does quantum physics have on the realm of causality? For instance, due to the wave-particle duality, is it reasonable to say that the universe can be explained through causality? How does this change the concept of 'logic'? Intuitively, we believe...
  22. P

    Valid and Invalid Logic Arguments: Explained

    Can anybody help me with the following arguments: 1) If 2+2=5 then 2+3=6 but,2+2=/=5 hence 2+3=/=6 2) If 2+2=4 then 2+3=6 but, 2+2=4 hence 2+3=6 3) if 2+2=5 then 2+3=6 but 2+3=/=6 hence 2+2=/=5 4) if 2+2=4 then 2+3=6 but, 2+3=/=6 hence 2+2=/=4 Which of the above are valid and...
  23. T

    Learning Logic to Master Math Proofs

    Would taking an intro to logic course help me prepare for the abstract proof writing skills that I'll need in upper division math?
  24. J

    Is my logic correct? - L. Algebra question

    Is my logic correct? -- L. Algebra question Homework Statement \left[ \begin{array}{cccc} 1 & 2 & -3 & 2 \\ -1 & -2 & b & 3 \\ 0 & 0 & c & 2 \end{array} \right] (1) For what values b and c is the system in the augmented matrix above consistent? (2) For what values b and c does the system in...
  25. C

    Uncertainty Principle logic help

    Does the uncertainty principle contradict the idea that an object can be at rest relative to an observer? For example, in physics class we examined an electron in a box, and we assumed the walls of the box are stationary relative to the observer. But the uncertainty principle says delta p...
  26. Fra

    Logic of E-H action, ricci scalar, cosmological constant?

    Logic of E-H action, ricci scalar, cosmological constant?? This crazy thread is mean to stimulate some reflections on the logic of Einsteins Equations. It would be interesting if those who have any ideas can join. Maybe it could be enlightning? The common way of thinking about GR is that we...
  27. N

    Solving Propositional Logic and Quantifier Expressions

    Not sure where to post this subject, so if it is in the wrong location please forgive. 1. Restore the parentheses to these abbreviated propositional forms? Q \wedge \backsim S \vee \backsim ( \backsim P \wedge Q ) I got this, but am not sure if it is correct. [Q \wedge (\backsim S)]...
  28. Fra

    Is Smolin's Approach to Quantum Gravity Logic Revolutionary?

    I finally started to read Smolin's Three roads to Quantum Gravity and only read the first two chapters so far. It doesn't contain any math, but it does seem to present a particular choice of reasoning on howto make progress on the matter, which I think is interesting in it's own because it may...
  29. N

    Can Fuzzy Logic Effectively Control Air Flow?

    i want application on fuzzy logic, from internet easy to understand
  30. T

    2nd order logic and mathematics?

    Does most of mathematics use 2nd order logic? If so would studying the foundations of mathematics involve mostly using 2nd order logic?
  31. N

    Understanding Fuzzy Logic: A Guide for Exam Preparation

    hello i want help me because i have exam
  32. D

    Symbolic logic, with truth table definition

    I don't really know if this is an acceptable topic to be placing in a "Sciences" homework help forum. It's a problem I'm having in my Symbolic Logic class. Homework Statement Every sentence has a truth-table which can describe it, does every truth table have a sentence? We're dealing...
  33. T

    A question about the logic of certain transformations

    there is this table that i showed in my previos question now i need to implement it using 16X4 and 4 X4 proms here is the table: http://s290.photobucket.com/albums/ll279/transgalactic/?action=view&current=IMG_8814.jpg here is the table...
  34. L

    Help with Translating English to Predicate Logic

    I have been asked to translate an argument from english into PL and show deductive validity through constructing a PL derivation. I have no problem constructing the derivation but this is the first time I have had to translate from English into PL. I am stuck and any help would be greatly...
  35. M

    How to Solve a Logic Problem with Numbers Using Equations?

    Homework Statement given a number of four ciphers ABCD and another four cipher number CDAB get the values of A,B,C,D if we know that 2x (ABCD)=CDAB-5 Homework Equations 2X (ABCD)=CDAB-5 The Attempt at a Solution no idea.. i have try by brute force but got no results only...
  36. A

    Can someone check my logic? simple harmonic motion.

    Homework Statement Is the daily movement of a student from home to school and back simple harmonic motion? Homework Equations The Attempt at a Solution I don't think it is. This type of movement is linear. It involves distance, speed and so on. It does not follow a sinusoidal...
  37. V

    Example exercises and answers for predicate logic inference (+ FOL in general)

    I'm battling with first order predicate logic (no identity, no extensions) and currently esp. inference using the so called "natural reasoning" rules for inference. Now, the textbook we use, is very ambiguously defined, even I have spotted several 'errors' in it, the lecturer even more. This...
  38. W

    Is logic ultimately constructed on faith?

    To me, there is no doubt that logic cannot be constructed if it isn't initiated by a set of unprovable 'rules', axioms, to be more precise. For example, I can't prove that a statement is either true or false under any circumstances, but I do assume this is consistently true - if a statement is...
  39. E

    Can u make if A>=B then output=1 Else output=0 using these logic gates?

    [SOLVED] can u make "if A>=B then output=1 Else output=0" using these logic gates? Homework Statement this is not quite a homework problem. I am designing a device and I need to use A>=B comparator. The challenge is I need to do this using only NAND, AND, NOR, OR and ExclusiveOR gates...
  40. J

    Deduction theorem for first order logic

    If I have P l- Q in FOL and P is closed, can I infer l- P -> Q. IIRC, this is valid as long as P is closed, but my memory is a little hazy. Is that how it works?
  41. R

    Diode Logic Gates circuit analysis?

    I need to understand how diode-resistor gates work. I've read a lot about what's supposed to happen based on inputs, but I need to see some numbers & analysis to understand what's going on. Where do you start in terms of trying to analyze the following AND gate...
  42. P

    Engineering ECE - logic circuit for a 4 bit input which counts 1s in input

    Homework Statement Using basic gates and/or building blocks, design a logic circuit that takes in a 4 bit input and will compute the number of 1s in the input. Homework Equations The Attempt at a Solution I have no idea where to start can anyone help please.
  43. S

    Negation of All Participants Being IT and Math Majors: Using Basic Logic Laws

    Homework Statement Use logic to write the negation of the sentence: All participants of this course are IT majors and are Math majors (be careful, use basic logic laws) Homework Equations DeMorgan's Law The Attempt at a Solution Letting P(x) be Participants who are IT majors...
  44. S

    Universal Quantifier & Material Conditionals in First Order Logic: Explained

    Can anyone tell me if the universal quantifier distributes over material conditionals in standard first order logic? Does (v)(Mv → Pv) imply {v)Mv -> (v)Pv? Does the implication work the other way too? Thanks.
  45. J

    Debugging Logic Flow: Tips and Tricks

    Never mind there, I screwed up my logic flow
  46. D

    LOGIC proving/disproving general laws

    One of the following general laws is true, the other false. Prove the true one. Find a counter example to the other.(We must do this in writing out each statement, no truth tables or anything. (a) If X implies Y, then the disjunction of X or Y is equivalent to X. (b) If X implies Y, then the...
  47. J

    What's up with the fuzzy logic

    When I first heard about the fuzzy logic, some guys told me that it would replace all "classical mathematics", being superior to it, but scientists are unfortunately reluctant to accept it yet. I immediately concluded, that fuzzy logic would be pseudo science. I later learned, that fuzzy...
  48. S

    Horses have heads Symbolic Logic

    "Horses have heads" Symbolic Logic I was given this sentence to represent in first-order predicate calculus. The formula must use the following terms--horse, has, head--where: "horse" represents "x is a horse" "has" represents "x has a head" "head" represents "x is a head" Are these...
  49. T

    A question in solving basic oprations in digital logic

    1. 11010101 / 11011 2. code each one of the deximal numbers by weight ( 6, 4, 2, -3 ) i don't know what the meen but some how i am sopposed to code using them 3. code the number 729 in excess3 code the number 729 in BCD code the number 729 in 2421 code i lack the theoretical knowledge to...
  50. cepheid

    Propositional Logic problem

    Homework Statement Richard is either a knight or a knave. Knights always tell the truth, and only the truth; knaves always tell falsehoods, and only falsehoods. Someone asks, "Are you a knight?" He replies, "If I am a knight, then I'll eat my hat." a) Must Richard eat his hat? b) Set this up...
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